%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : NUM523+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 14:27:06 EDT 2022
% Result : Theorem 0.78s 0.93s
% Output : Refutation 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 24 ( 12 unt; 2 nHn; 24 RR)
% Number of literals : 56 ( 0 equ; 35 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
aNaturalNumber0(xn),
file('NUM523+3.p',unknown),
[] ).
cnf(4,axiom,
aNaturalNumber0(xm),
file('NUM523+3.p',unknown),
[] ).
cnf(5,axiom,
aNaturalNumber0(xp),
file('NUM523+3.p',unknown),
[] ).
cnf(6,axiom,
isPrime0(xp),
file('NUM523+3.p',unknown),
[] ).
cnf(18,axiom,
( ~ skC0
| ~ doDivides0(xp,xn) ),
file('NUM523+3.p',unknown),
[] ).
cnf(27,axiom,
equal(sdtasdt0(xp,sdtasdt0(xm,xm)),sdtasdt0(xn,xn)),
file('NUM523+3.p',unknown),
[] ).
cnf(29,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| aNaturalNumber0(sdtasdt0(v,u)) ),
file('NUM523+3.p',unknown),
[] ).
cnf(33,axiom,
( ~ aNaturalNumber0(u)
| ~ equal(sdtasdt0(xp,u),sdtasdt0(xn,xn))
| skC0 ),
file('NUM523+3.p',unknown),
[] ).
cnf(57,axiom,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ equal(u,sdtasdt0(v,w))
| doDivides0(v,u) ),
file('NUM523+3.p',unknown),
[] ).
cnf(76,axiom,
( ~ isPrime0(u)
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| ~ aNaturalNumber0(w)
| ~ doDivides0(u,sdtasdt0(w,v))
| doDivides0(u,v)
| doDivides0(u,w) ),
file('NUM523+3.p',unknown),
[] ).
cnf(118,plain,
( ~ aNaturalNumber0(u)
| ~ equal(sdtasdt0(xp,u),sdtasdt0(xn,xn)) ),
inference(spt,[spt(split,[position(s1)])],[33]),
[iquote('1:Spt:33.0,33.1')] ).
cnf(149,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ equal(sdtasdt0(xn,xn),sdtasdt0(xn,xn)) ),
inference(spl,[status(thm),theory(equality)],[27,118]),
[iquote('1:SpL:27.0,118.1')] ).
cnf(151,plain,
~ aNaturalNumber0(sdtasdt0(xm,xm)),
inference(obv,[status(thm),theory(equality)],[149]),
[iquote('1:Obv:149.1')] ).
cnf(164,plain,
$false,
inference(ssi,[status(thm)],[151,29,4]),
[iquote('1:SSi:151.0,29.0,4.0,4.2')] ).
cnf(174,plain,
skC0,
inference(spt,[spt(split,[position(s2)])],[33]),
[iquote('1:Spt:164.0,33.2')] ).
cnf(175,plain,
~ doDivides0(xp,xn),
inference(mrr,[status(thm)],[18,174]),
[iquote('1:MRR:18.0,174.0')] ).
cnf(649,plain,
( ~ aNaturalNumber0(sdtasdt0(u,v))
| ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| doDivides0(u,sdtasdt0(u,v)) ),
inference(eqr,[status(thm),theory(equality)],[57]),
[iquote('0:EqR:57.3')] ).
cnf(658,plain,
( ~ aNaturalNumber0(u)
| ~ aNaturalNumber0(v)
| doDivides0(u,sdtasdt0(u,v)) ),
inference(ssi,[status(thm)],[649,29]),
[iquote('0:SSi:649.0,29.2')] ).
cnf(693,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(spr,[status(thm),theory(equality)],[27,658]),
[iquote('0:SpR:27.0,658.2')] ).
cnf(714,plain,
doDivides0(xp,sdtasdt0(xn,xn)),
inference(ssi,[status(thm)],[693,29,4,6,5]),
[iquote('0:SSi:693.1,693.0,29.0,4.0,4.0,6.0,5.2')] ).
cnf(2503,plain,
( ~ isPrime0(xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn)
| doDivides0(xp,xn)
| doDivides0(xp,xn) ),
inference(res,[status(thm),theory(equality)],[714,76]),
[iquote('0:Res:714.0,76.4')] ).
cnf(2508,plain,
( ~ isPrime0(xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| doDivides0(xp,xn) ),
inference(obv,[status(thm),theory(equality)],[2503]),
[iquote('0:Obv:2503.4')] ).
cnf(2509,plain,
doDivides0(xp,xn),
inference(ssi,[status(thm)],[2508,3,6,5]),
[iquote('0:SSi:2508.2,2508.1,2508.0,3.0,6.0,5.0,6.0,5.0')] ).
cnf(2510,plain,
$false,
inference(mrr,[status(thm)],[2509,175]),
[iquote('1:MRR:2509.0,175.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM523+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n011.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jul 5 02:09:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.78/0.93
% 0.78/0.93 SPASS V 3.9
% 0.78/0.93 SPASS beiseite: Proof found.
% 0.78/0.93 % SZS status Theorem
% 0.78/0.93 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.78/0.93 SPASS derived 1395 clauses, backtracked 46 clauses, performed 6 splits and kept 668 clauses.
% 0.78/0.93 SPASS allocated 100026 KBytes.
% 0.78/0.93 SPASS spent 0:00:00.56 on the problem.
% 0.78/0.93 0:00:00.03 for the input.
% 0.78/0.93 0:00:00.04 for the FLOTTER CNF translation.
% 0.78/0.93 0:00:00.02 for inferences.
% 0.78/0.93 0:00:00.00 for the backtracking.
% 0.78/0.93 0:00:00.43 for the reduction.
% 0.78/0.93
% 0.78/0.93
% 0.78/0.93 Here is a proof with depth 3, length 24 :
% 0.78/0.93 % SZS output start Refutation
% See solution above
% 0.78/0.93 Formulae used in the proof : m__2987 m__3025 m__ m__3014 mSortsB_02 mDefDiv mPDP
% 0.78/0.93
%------------------------------------------------------------------------------